Set off, having appointment outside famous school (8)
I believe the answer is:
detonate
'set off' is the definition.
(synonyms)
'appointment outside famous school' is the wordplay.
'appointment' becomes 'date' (synonyms).
'outside' means one lot of letters goes inside another.
'famous school' becomes 'eton' (I've seen this before).
'date' placed around 'eton' is 'DETONATE'.
'having' acts as a link.
(Other definitions for detonate that I've seen before include "go off with a bang" , "Blow up, explode" , "Discharge" , "Cause to explode" , "Trigger" .)